Suppose that in a certain culture, the equation Q(t)= 1000...

Suppose that in a certain culture, the equation $Q(t)=$ $1000 e^{0.4 t}$ expresses the number of bacteria present as a function of the time $t$, where $t$ is expressed in hours. How many bacteria are present at the end of 2 hours? 3 hours? 5 hours? $2226 ; 3320 ; 7389$

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Key Concepts

Exponential Growth Model

This concept describes situations where the rate of change of a quantity is proportional to the current amount, leading to exponential increases or decreases over time. It is typically represented by functions of the form Q(t) = Q?e^(rt), where Q? is the initial value and r is the growth rate. Such models are applicable in various fields including biology, finance, and physics.

Natural Exponential Function

The natural exponential function, denoted as e^(x), is fundamental in modeling continuous change. With the constant e approximately equal to 2.71828, its unique property of having a derivative equal to itself makes it ideal for describing processes like continuous growth or decay in mathematical models.

Function Evaluation through Substitution

This key process involves replacing the variable in a function with specific values to determine the output at those instances. In the context of growth models, substituting given time values into the exponential function allows one to calculate the corresponding quantity, such as the number of bacteria at a particular time.

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